A uniform rod AB of mass 3m and length 2l is lying at rest on a smooth horizontal table with a smooth vertical axis through the end A. A particle of mass 2m moves with speed 2u across the table and strikes the rod at its mid-point C if the impact is perfectly elastic. Find the speed of the particle after impact if
(a). It strikes rod normally,
(b). Its path before impact was inclinded at `60^(@)` to AC.

Explanation

To solve the problem step by step, we will analyze both parts of the question systematically.

### Given:
- Mass of the rod, \( m_{rod} = 3m \)
- Length of the rod, \( L_{rod} = 2l \)
- Mass of the particle, \( m_{particle} = 2m \)
- Initial speed of the particle, \( u_{initial} = 2u \)
- The collision is perfectly elastic.
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